I'm in Spain and my partner had a sudden onset of floaters a few months ago. It was at the weekend and we couldn't see a normal doctor, so we went to the A&E department of a large hospital in our city, and the ophthalmologists there saw him. This was all covered by the state system in Spain. However, if we had gone to the GP and waited to be referred, it would have taken a long time. Every country had a different system though, so I don't know what would be best in your case. Do they charge for A&E (ER) visits where you live?

Anyway, just for peace of mind, I would try to see someone soon.